Geostatistical and morphological methods applied to three-dimensional microscopy

Three-dimensional (3-D) images of osteocyte lacunae were examined on a confocal microscope. Both geostatistical and morphological processing techniques were used to improve and to analyse them. By a geostastical approach, this study aims at improving 3-D confocal images before any further image processing. Optimized linear filters, which take account of the second-order statistics and the 3-D structure of the data, allow for the removal of imperfections such as noise and/or blur due to the axial convolution, and interpolate voxels on a face-centred cubic grid from an initial cubic grid. An application of this technique to 3-D biological images is demonstrated. In a second step, a 3-D binary image is digitized and cleaned with 3-D morphological filters. The standard 3-D measurements cannot be applied in this case, since all osteocytes cut the border of the field. For this reason a 3-D Boolean model has been adjusted, from which it is possible to derive all useful information on the repartition and the morphology of the osteocytes.